1. Field of the Invention
The present invention relates to an image processing apparatus, and specifically relates to an image processing apparatus and an imaging apparatus which executes a restoration process regarding images, and a processing method according to these, and a program that causes a computer to execute the method thereof.
2. Description of the Related Art
Heretofore, a deteriorated image restoration process wherein a deteriorated image is restored has been widely familiar as an image processing technique. For example, in a case where a deteriorated model of an image and an observed image are known, this deteriorated image restoration process is a process wherein a subject image is restored from an observed image including deterioration. For example, in the case of assuming that a model of an observed image g, a deterioration matrix h, and noise n shown in Expression 1 are known, a subject image f shown in Expression 1 can be obtained.
                    g        =                              h            ⊗            f                    +          n                                    Expression        ⁢                                  ⁢        1                                          error          2                =                                                                        h                ⊗                                  f                  ^                                            -              g                                            2                                    Expression        ⁢                                  ⁢        2                                                      f            ^                                k            +            1                          =                                            f              ^                        k                    +                      λ            ⁢                                                  ⁢                                          h                T                            ⁡                              (                                                      h                    ⊗                                                                  f                        ^                                            k                                                        -                  g                                )                                                                        Expression        ⁢                                  ⁢        3                                                      f            ^                                k            +            1                          =                                            f              ^                        k                    (                      h            ⁢                          g                              h                ⊗                                                      f                    ^                                    k                                                              )                                    Expression        ⁢                                  ⁢        4                                                      f            ^                                k            +            1                          =                                            f              ^                        k                    +                      a            ⁡                          (                                                h                  ⊗                                                            f                      ^                                        k                                                  -                g                            )                                                          Expression        ⁢                                  ⁢        5                                                      f            ^                                k            +            1                          =                                            f              ^                        k                    (                      b            ⁢                          g                              h                ⊗                                                      f                    ^                                    k                                                              )                                    Expression        ⁢                                  ⁢        6            
There is a method to solve this problem as a problem to minimize an error between an observed image and an estimated deteriorated image which is obtained as a convolution result of a deterioration matrix h and an estimated subject image f^ (shown in Expression 2), as one solution of this problem.
Also, as an iterative solution for this minimization problem, there are the Back-projection method shown in Expression 3 (e.g., “Landweber” in Patrizio Campisi, Karen Egiazarian: “Blind Image Deconvolution—Theory and Application”, CRC Press, pp 288-289 (see (7.34) and (7.35) and others), and the Lucy-Richardson method shown in Expression 4 (e.g., see Patrizio Campisi, Karen Egiazarian: “Blind Image Deconvolution—Theory and Application”, CRC Press, pp 288-289 (see (7.34) and (7.35) and others)). These are methods wherein an observed image and an estimated deteriorated image are compared by subtraction or division, and the obtained error and the value of a ratio are fed back to a restored image. With these methods, there are terms of products by employing a blurring matrix and a constant λ at the time of this feedback, but there is also a method wherein these are taken as an arbitrary matrix a or b (shown in Expression 5 and Expression 6).